State and Local Public Finance Professor Yinger Spring 2019

State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Section Outline This is the first of three classes on public sector costs 1. Production and Cost Concepts 2. Policies to Lower Costs 3. Case: Lockup Quotas These classes are about the technology of public production.

Class Outline Public Production and Cost Functions State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Class Outline Public Production and Cost Functions The Role of the “Environment” Cost and Efficiency

Key Concepts Production functions translate inputs into outputs. State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Key Concepts Production functions translate inputs into outputs. Cost functions indicate the spending required to reach a given level of output. Understanding public production and cost functions is critical to understanding public spending and performance.

Private Production and Cost State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Private Production and Cost Private Production Function Q = q{Inputs} Private Cost Function C = c{Q, Input Prices}

Government Production Function State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Government Production Function (Bradford/Malt/Oates, National Tax Journal 1969) Intermediate Output (G depends on inputs) G = g{Inputs} Final Output (S depends on G and the Environment, N) S = s{G, Environment} = s{G, N} Inverted Final Output (required G depends on N and on desired S) G = s-1{S, N}

Government Cost Functions (B/M/O, NTJ 1969) State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Government Cost Functions (B/M/O, NTJ 1969) Cost of Intermediate Output (depends on G and input prices, W) CG = cG{G, W} Cost of Final Output (depends on S, N, and W) C = c{G needed for S, W} = c{s-1{S, N}, W} = cʹ{S, N, W}

State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Public Outputs Public cost functions focus on the cost of government performance. Police: Crime rate. Fire: Probability of loss from fire. Education: Test scores, graduation rates. Public cost functions are influenced by the environment in which the services are delivered.

Examples of “Environment” State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Examples of “Environment” Police: Poor people are more likely to be victims of crime and to be desperate enough to turn to crime. Fire: Old houses catch fire more often and burn faster; fire spreads faster when housing is closely packed. Education: Children from poor families are more likely to bring health or behavioral problems to school, and less likely to have lessons reinforced at home.

Estimates of “Environment” State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Estimates of “Environment” Ladd & Yinger (America’s Ailing Cities 1991) find that police costs increase with poverty and city population. Duncombe & Yinger (Journal of Public Economics 1993) find that fire costs increase with industrial and utility property and tall buildings. Many scholars find that education costs increase with the share of students from poor families or with limited English proficiency. (See, for example, Duncombe and Yinger, Economics of Education Review 2005).

Estimated Pupil Weights (=extra costs for at-risk pupils) State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Estimated Pupil Weights (=extra costs for at-risk pupils)   Simple Average Pupil- Weighted Average Directly Estimated Without Special Education Child Poverty 1.415 1.491 1.667 LEP 1.007 1.030 1.308 With Special Education 1.224 1.281 1.592 1.009 1.033 1.424 Special Education 2.049 2.081 2.644 From: Duncombe/Yinger EER 2005

Duncombe/Yinger Study of California State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Duncombe/Yinger Study of California (International Tax and Public Finance 2011) Cost factors in education Share of student from poor families Share of students with limited English proficiency Share of students with a severe disability Required wage to attract teachers Enrollment (economies of scale) Enrollment change Grade level (higher costs for high school)

State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Cost versus Spending A cost function describes technology, and implicitly is based on best practices. In fact, however, we cannot observe costs, we can only observe spending. The final step in the logic is to link costs and spending.

Government Expenditure Function State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Government Expenditure Function To link cost (C) and spending (E), we can write: E = C/e = c{S, N, W}/e Definition of Efficiency (e) An efficient government (e = 1) uses best practices to spend as little as possible in delivering S. Spending more than this minimum (e < 1) is inefficient. Alternative measures of S yield alternative definitions of e.

Examples of Efficiency State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Examples of Efficiency Suppose we define S as student performance on basic math and reading tests. Many rich, suburban schools will be inefficient despite their high scores because they spend a lot on art, music, science, and social studies. Some poor, urban schools will be efficient despite their low scores because they focus most of their spending on the basics. Some schools also may be inefficient because they are wasteful—a type of inefficiency that cannot be separated from the above.

Measuring Efficiency Efficiency cannot be measured directly. State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Measuring Efficiency Efficiency cannot be measured directly. Scholars disagree on the best way to account for efficiency in estimating an expenditure function. One method (D/Y): The efficiency-related behavior of voters (monitoring, demand for public services not in S) and public officials (waste) responds to incentives. Control for variables that describe these incentives.

Examples of Incentives That May Influence Efficiency State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Examples of Incentives That May Influence Efficiency Tax Price: Voters monitor public officials more carefully when paying a higher share of tax revenue. State Aid: State aid shifts the financing burden away from voters and weakens their incentive to monitor public officials. Competition: Public officials may be more efficient when they face competition.

Duncombe/Yinger Study of California State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Duncombe/Yinger Study of California Efficiency factors in education (with state’s test score index as the measure of performance) Median income Tax price (based on parcel tax) State aid for education Federal aid for education Migration into district Categorical aid as a share of total aid

Other Recent Cost Studies State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Other Recent Cost Studies New York: Eom, Duncombe, Nguyen-Hoang, and Yinger, Education Finance and Policy, Fall 2014. Massachusetts: Nguyen-Hoang and Yinger. Journal of Education Finance, Spring 2014.   Missouri: Duncombe and Yinger, Peabody Journal of Education, 2011. California, Kansas, Missouri, and New York: Lukemeyer, Duncombe, and Yinger. In Improving on No Child Left Behind, R. D. Kahlenberg (ed.), The Century Foundation, 2008.

Allocative versus Productive Efficiency State and Local Public Finance Lecture 4: Public Sector Costs: Concepts Allocative versus Productive Efficiency Note that we have defined two different efficiency concepts: Allocative efficiency = whether goods and services are allocated to the people who value them most Productive efficiency = whether goods and services are produced using best practices You can improve public welfare by boosting either type of efficiency!